Algebra Examples

$\sqrt{- 2^{2} + - 2^{2}}$

Step 1

Replace all occurrences of $+$ $-$ with a single $-$ . A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign because $1 \cdot - 1 = - 1$

$\sqrt{- 2^{2} - 2^{2}}$

Step 2

Simplify the expression.

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Step 2.1

Raise $2$ to the power of $2$ .

$\sqrt{- 1 \cdot 4 - 2^{2}}$

Step 2.2

Multiply $- 1$ by $4$ .

$\sqrt{- 4 - 2^{2}}$

Step 2.3

Raise $2$ to the power of $2$ .

$\sqrt{- 4 - 1 \cdot 4}$

Step 2.4

Multiply $- 1$ by $4$ .

$\sqrt{- 4 - 4}$

Step 2.5

Subtract $4$ from $- 4$ .

$\sqrt{- 8}$

Step 3

Rewrite $- 8$ as $- 1 (8)$ .

$\sqrt{- 1 (8)}$

Step 4

Rewrite $\sqrt{- 1 (8)}$ as $\sqrt{- 1} \cdot \sqrt{8}$ .

$\sqrt{- 1} \cdot \sqrt{8}$

Step 5

Rewrite $\sqrt{- 1}$ as $i$ .

$i \cdot \sqrt{8}$

Step 6

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 6.1

Factor $4$ out of $8$ .

$i \cdot \sqrt{4 (2)}$

Step 6.2

Rewrite $4$ as $2^{2}$ .

$i \cdot \sqrt{2^{2} \cdot 2}$

Step 7

Pull terms out from under the radical.

$i \cdot (2 \sqrt{2})$

Step 8

Move $2$ to the left of $i$ .

$2 i \sqrt{2}$